#!/usr/bin/perl -w # Copyright 2010, 2011, 2012 Kevin Ryde # This file is part of Math-PlanePath. # # Math-PlanePath is free software; you can redistribute it and/or modify it # under the terms of the GNU General Public License as published by the Free # Software Foundation; either version 3, or (at your option) any later # version. # # Math-PlanePath is distributed in the hope that it will be useful, but # WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY # or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License # for more details. # # You should have received a copy of the GNU General Public License along # with Math-PlanePath. If not, see . # Usage: perl hilbert-oeis.pl # # This spot of code prints sequence A163359 of Sloane's On-Line Encyclopedia # of Integer Sequences # # http://oeis.org/A163359 # # which is the Hilbert curve N values which occur on squares numbered # diagonally in the style of Math::PlanePath::Diagonals, # # 0, 3, 1, 4, 2, 14, 5, 7, 13, 15, 58, 6, 8, 12, 16, 59, ... # # All points in the first quadrant are reached by both paths, so this is a # re-ordering or the non-negative integers. # # In the code there's a double transpose going on. A163359 is conceived as # the Hilbert starting downwards and the diagonals numbered from the X axis, # but the HilbertCurve code goes to the right first and the Diagonals module # numbers from the Y axis. The effect is the same, ie. that the first # Hilbert step is the opposite axis as the diagonals are numbered from. # # Diagonals option direction=>up could be added to transpose \$x,\$y to make # the first Hilbert step the same axis as the diagonal numbering. Doing so # would give sequence A163357. # use 5.004; use strict; use Math::PlanePath::HilbertCurve; use Math::PlanePath::Diagonals; my \$hilbert = Math::PlanePath::HilbertCurve->new; my \$diagonal = Math::PlanePath::Diagonals->new; print "A163359: "; foreach my \$n (\$diagonal->n_start .. 19) { my (\$x, \$y) = \$diagonal->n_to_xy (\$n); # X,Y points by diagonals my \$hilbert_n = \$hilbert->xy_to_n (\$x, \$y); # hilbert N at those points print "\$hilbert_n, "; } print "...\n"; exit 0;